JSFiddle - React, Tailwind, and code Playground
HTML
<input id="clickMe" value="clickme" type="button" />
<select id="dropdown">
<option value="0">Select Fields</option>
</select>
JavaScript
$i=0;
$("#clickMe").click(function(e){
$i++;
$("#dropdown").append("<option value='"+$i+"'>New Field</option>");
});